The sum of the first $6$ terms of a geometric series is $15{,}624$ and the common ratio is $5$. What is the first term of the series?
Explanation: This formula gives the sum ${S_n}$ of the first $ n$ terms in the geometric series where the first term is $ a$ and the common ratio is $C r$ : ${S_n}=\dfrac{ a(1-C r^{ n})}{1-C r}$ We are given the values for ${S_n}$, $ n$, and $C r$.Let's plug them in the formula and solve for $ a$. We are given that ${S_n=15{,}624}$, ${n=6}$, and $C{r=5}$ : ${15{,}624}=\dfrac{ a(1-C 5^{{6}})}{1-C 5}$ Solving the equation, we get that $a=4$. In conclusion, the first term of the series is $4$.